Question

Let Q(p) be the demand function for a certain product, where p is price. If R is a function of p for the total revenue, (dR)/(dp)

MR=

Your answer should be In terms of Q and E

Answer 1

Elasticity is denoted by E, so the formula of elasticity is :

^{E =}

Here, we have to find MR in terms of Q and E

Given, Q(p) be the demand function for a certain product, where p is price.

If R is a function of p for the total revenue

It means R = p*Q(p)

And (dR)/(dp) is MR so MR will be, solving dR/dp we get,

MR = p * Q'(p) + Q(p)

But we want the MR in terms of Q and E

And we know that p' = and Q'(p) = , it means

MR = +

And we can write E as

  ^{[ ]}

Now put value of in MR we get,

MR = +

=

[as p' = dp/dp =1 so =1]

MR = Q(E+1)

MR = Q*E + Q

(Here MR in the form of Q and E)